Wireless communications are a ubiquitous part of modern life in many areas. One well known and widely deployed wireless communication protocol is Code Division Multiple Access (CDMA). CDMA networks use spread-spectrum technology, encoding (spreading) data for different users with different, orthogonal codes, and transmitting the higher-bandwidth encoded signals over the same frequency. In a CDMA system, each code sequence comprises a separate communication channel. Known reference symbols, called pilot symbols, are transmitted over a separate channel from the data symbols (that is, spread with a different code than the data symbols). Receivers use the pilot channel to estimate required receiver quantities.
Note that estimates obtained from the pilot channel are scaled according to the pilot channel power, which is typically significantly higher than the data channel power(s). Receiver operations that require estimates scaled according to the data channel power may obtain properly scaled estimates through the use of the data to pilot power ratio. For example, the pilot channel may be used to estimate the net channel coefficients (hpilot=√{square root over (Ep)}h). Some receiver operations require an estimate of the net channel coefficients scaled according to the data channel power (hdata=√{square root over (Ed)}h). Using the relationship hdata=ghpilot, where g=√{square root over (Ed/Ep)} (i.e., the square root of the data to pilot power ratio), the receiver can obtain the net channel estimates with the proper scaling.
The data to pilot power ratio is useful in many contexts. An example is soft value scaling for turbo decoding. For 16 QAM and 64 QAM constellations, the log-likelihood of bit bj can be written
                              LLR          ⁡                      (                          b              j                        )                          =                                            ∑                                                s                  i                                ⁢                                                      εS                    0                                    ⁡                                      (                    j                    )                                                                        ⁢                                                  ⁢                          exp              ⁢                              {                                  γ                  ⁡                                      (                                                                  2                        ⁢                                                                                                  ⁢                                                  Re                          ⁡                                                      (                                                                                                                            s                                  i                                  *                                                                ⁢                                z                                                                                                                              w                                  H                                                                ⁢                                                                  h                                  data                                                                                                                      )                                                                                              -                                                                                                                              s                            i                                                                                                    2                                                              )                                                  }                                                                        ∑                                                s                  i                                ⁢                                                      εS                    1                                    ⁡                                      (                    j                    )                                                                        ⁢                                                  ⁢                          exp              ⁢                              {                                  γ                  ⁡                                      (                                                                  2                        ⁢                                                                                                  ⁢                                                  Re                          ⁡                                                      (                                                                                                                            s                                  i                                  *                                                                ⁢                                z                                                                                                                              w                                  H                                                                ⁢                                                                  h                                  data                                                                                                                      )                                                                                              -                                                                                                                              s                            i                                                                                                    2                                                              )                                                  }                                                                        (        1        )            where z represents an estimated symbol value, si is an actual symbol value, γ is the signal to noise ratio, and w is a vector of combining weights. Using the data to pilot power ratio and the pilot-based channel estimates, equation (1) can be evaluated via
                              LLR          ⁡                      (                          b              j                        )                          =                                            ∑                                                s                  i                                ⁢                                                      εS                    0                                    ⁡                                      (                    j                    )                                                                        ⁢                                                  ⁢                          exp              ⁢                              {                                  γ                  ⁡                                      (                                                                  2                        ⁢                                                                                                  ⁢                                                  Re                          ⁡                                                      (                                                                                                                            s                                  i                                  *                                                                ⁢                                z                                                                                                                              gw                                  H                                                                ⁢                                                                  h                                  pilot                                                                                                                      )                                                                                              -                                                                                                                              s                            i                                                                                                    2                                                              )                                                  }                                                                        ∑                                                s                  i                                ⁢                                                      εS                    1                                    ⁡                                      (                    j                    )                                                                        ⁢                                                  ⁢                          exp              ⁢                              {                                  γ                  ⁡                                      (                                                                  2                        ⁢                                                                                                  ⁢                                                  Re                          ⁡                                                      (                                                                                                                            s                                  i                                  *                                                                ⁢                                z                                                                                                                              gw                                  H                                                                ⁢                                                                  h                                  pilot                                                                                                                      )                                                                                              -                                                                                                                              s                            i                                                                                                    2                                                              )                                                  }                                                                        (        2        )            
Another receiver operation that requires accurate data to pilot power ratio is Signal to Interference and Noise Ratio (SINR) estimation. Co-pending U.S. patent application, “Data-Aided SIR Estimation,” by Rosenqvist, et al., filed concurrently with the present application, assigned to the assignee of the present application, and incorporated herein by reference in its entirety, discloses the use of estimated data symbols to improve the reliability and accuracy of SINR estimates. The general approach is
1. obtain estimated data symbols;
2. normalize the symbols to match the power of the transmitted constellation (alternatively, scale a reference constellation to match the power of the received data);
3. determine the closest constellation point for each estimated data symbol (i.e. hard symbol decisions);
4. determine signal power as the average power of the detected constellation points;
5. determine noise power as the average power of the difference between the scaled data symbols and the detected constellation points; and
6. correct for bias caused by incorrect hard symbol decisions.
Step 2 in this procedure requires the normalization of the data symbols. An estimated data symbol value can be written as
                                                                        z                k                            =                                                                    w                    H                                    ⁢                                      h                    data                                    ⁢                                      s                    k                                                  +                                  u                  k                                                                                                        =                                                As                  k                                +                                  u                  k                                                                                        (        3        )            so the proper normalization factor is A=wHhdata. Using the data to pilot power ratio and the pilot-based channel coefficients, a good estimate of A can be obtained fromA=gwHhpilot.  (4)
A number of methods for determining the data to pilot power ratio are known in the art. Co-pending U.S. patent application Ser. No. 11/064,351, “A Method and Apparatus for Estimating Gain Offsets for Amplitude-Modulated Communication Signals,” by Cairns, filed Feb. 23, 2005, assigned to the assignee of the present application and incorporated herein by reference in its entirety, provides an overview of the methods known up to 2004, and the drawbacks of each of them. Two additional approaches have been explored since 2004.
One approach is the Algebraic Solution. The data to pilot power ratio can be obtained via
                              g          =                                                                      E                  ⁢                                      {                                          zz                      *                                        }                                                  -                                                      w                    H                                    ⁢                                      h                    pilot                                                                                                                                                            w                      H                                        ⁢                                          h                      pilot                                                                                        2                                                    ⁢                                  ⁢        where                            (        5        )                                          E          ⁢                      {                          zz              *                        }                          =                              1            CK                    ⁢                                    ∑                              c                =                0                                                              N                  c                                -                1                                      ⁢                                                  ⁢                                          ∑                                  k                  =                  0                                                  K                  -                  1                                            ⁢                                                                                          z                      k                      c                                        ⁡                                          (                                              z                        k                        c                                            )                                                        *                                .                                                                        (        6        )            Here, zkc is the kth estimated data symbol corresponding to code c, C is the number of codes used, and K is the number of data symbols per slot.
The main shortcoming of the Algebraic Solution is that the numerator of equation (5) tends to be quite noisy. A noisy numerator necessarily means noisy data to pilot power estimates. This leads to degraded performance for turbo decoding and SINR estimation. The numerator is noisy primarily for two reasons. First, there is an assumption that w=Ru−1hpilot. This is true only for a G-Rake (Generalized Rake) receiver, and only if the combining weights are determined exactly. In practice, some sort of iterative approach for determining w is generally used, so the combining weights are not exact. The second reason the numerator is noisy is that the pilot-based net channel estimates use a limited number of symbols. The noise due to estimation error can be substantial, especially when the SINR is low. Accordingly, in practice, the Algebraic Solution does not yield accurate data to pilot power ratio estimates.
Another approach is the Parametric G-Rake solution, wherein the data to pilot power ratio is determined as a by-product of determining the scaling factors for a parametric G-Rake receiver. Typically, a parametric G-Rake receiver uses an estimate of the impairment covariance matrix obtained from the pilot channel to determine the scaling factors. U.S. Pat. No. 7,590,167, “A Method and Apparatus for QAM Demodulation in a Generalized Rake Receiver,” by Fulghum, et al., issued Sep. 15, 2009, assigned to the assignee of the present application and incorporated herein by reference in its entirety, discloses the use of the data covariance matrix. The utility of this approach can be seen by writing the components of the data covariance matrix
                              R          d                =                              α            ⁢                                                  ⁢                          R              I                                +                      β            ⁢                                                  ⁢                          R              n                                +                                                    E                d                                            E                p                                      ⁢                          h              pilot                        ⁢                          h              pilot              H                                                          (        7        )            When the scale factors are determined by the least squares fitting procedure described in the '167 patent, an estimate of the data to pilot power ratio is obtained as a by-product. However, this method only applies to G-Rake receivers.